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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

3 votes
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Function and distance on bounded set [closed]

Does there exist a bounded set $A \subset \mathbb{R}^ n$ (for some $n$) and a function $f:A\to A$ (not necessarily onto) such that $\forall x,y \in A$ then $\|x-y\| < \|f(x)-f(y)\|$? If such a set $ …
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